Of course the last image is a fractal, it has a fractal structure as found in the Hénon attractor.  There doesn't exist a special name for it and that's not necessary.  We only use a relative small part of the large field of fractals.  More theory of the Hénon attractor can be found in many books, for instance Peitgens, Jürgens, Saupe: 'Fractals for the Classroom, part 2'.

Ed Algra